Termination w.r.t. Q of the following Term Rewriting System could be proven:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(g(f(a), h(a, f(a)))) → f(h(g(f(a), a), g(f(a), f(a))))
Q is empty.
↳ QTRS
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
f(g(f(a), h(a, f(a)))) → f(h(g(f(a), a), g(f(a), f(a))))
Q is empty.
Using Dependency Pairs [1,15] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:
F(g(f(a), h(a, f(a)))) → F(h(g(f(a), a), g(f(a), f(a))))
The TRS R consists of the following rules:
f(g(f(a), h(a, f(a)))) → f(h(g(f(a), a), g(f(a), f(a))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
F(g(f(a), h(a, f(a)))) → F(h(g(f(a), a), g(f(a), f(a))))
The TRS R consists of the following rules:
f(g(f(a), h(a, f(a)))) → f(h(g(f(a), a), g(f(a), f(a))))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 0 SCCs with 1 less node.